Dynamic Viscoelastic Effects on Free Vibrations of a Submerged Fluid-filled Thin Cylindrical Shell

Abstract

The novel features of the Havriliak-Negami model for dynamic description of viscoelastic material behavior along with the Donnell theory of shell motion are applied to study free vibrational and damping characteristics of an infinitely long viscoelastic thin circular cylindrical shell submerged in and filled with acoustic fluids. The analytical results are illustrated with numerical examples in which two fluid-filled shells of distinctive viscoelastic material properties are undergoing free vibrations in a surrounding ideal fluid medium. The natural frequencies and the associated modal loss factors as a function of the circumferential mode number at selected axial wave lengths and submergence conditions are numerically evaluated and discussed. The numerical results reveal the imperative influence of dynamic viscoelastic properties on the vibrational characteristics of the fluid-coupled system. They demonstrate an interesting correlation between the modal loss factor and the material loss factor in the vicinity of the calculated natural frequency. In particular, the modal loss factor (natural frequency) is found to be highly dependent on (fairly insensitive to) the frequency dependence of the loss factor in the viscoelastic material. A limiting case involving a thin elastic steel shell submerged in water is considered and fair agreement with a well-known solution is established.